The Seven Noahide laws are general commandments with many details. Transgressing any one of them is considered such a breach in the natural order that the offender incurs the death penalty. Apart from a few exceptions, the death sentence for a Ben Noach is Sayif, death by the sword / decapitation, the least painful of the four modes of execution of criminals (see the Rambam's Hilchos Melachim 9:14). (The four methods of capital punishment in Torah are: S’kilah - Stoning; S’rifah - Burning; Hereg - Decapitation; Henek - Strangulation.) The many formalities of procedure essential when the accused is an Israelite need not be observed in the case of the Noachite. The latter may be convicted on the testimony of one witness, even on that of relatives, but not on that of a woman. He need have had no warning from the witnesses; and a single judge may pass sentence on him (Sanhedrin 57a, b; Rambam, Hilchos Melakim 9:14).
Besides these seven major Mitzvos, Chazal received a tradition that there are other Mitzvos and prohibitions that are incumbent upon Benei Noach. The Beraisa in Sanhedrin 56b, notes certain Tana'im who rule that other prohibitions are incumbent upon Benei Noach. These prohibitions are:
Hebrew Transliteration English Translation Talmud
1 Dam Min ha'Chai not to eat blood that is taken from an animal when it is alive Rabbi Chananyah ben Gamliel said: Also not to partake of the blood drawn from a living animal
2 Sirus not to perform castration/emasculation Rabbi Chidka said, they are also forbidden to castrate
3 Kishuf witchcraft Rabbi Shimon said, also Kishuf (witchcraft /sorcery) is forbidden to them.
Rabbi Yossi said, everything in the Parshah of Kishuf is forbidden to them (Deut. / Devarim 18:10-11)
4 Harba'as Behemah mating different species of animals Rabbi Eliezer added Kilayim (forbidden mixture) in plants and animals. They are permitted to wear Sha'atnez - garments of mixed fabrics [of wool and linen] and sow diverse seeds together; they are forbidden only to hybridize heterogeneous animals and graft trees of different kinds.
5 Harkavas ha'Ilan grafting trees
The Amora'im add two more prohibitions:
1. Keeping Shabbos, that is, choosing a day of the week on which to refrain from work (Sanhedrin 58b).
2. Learning Torah other than the portions that deal with the seven major Mitzvos above (San. 59a).
The Rambam in Hilchos Melachim 8:11, writes that all Benei Noach who accept upon themselves the Seven Mitzvos and are careful to keep them and are precise in their observance are termed 'Chasidei Umos ha'Olam' מֵחֲסִידֵי אֻמּוֹת הָעוֹלָם ('the Pious Ones of the Nations') and they merit a share in the World to Come. However, they must keep these Mitzvos specifically because HaShem (G-d) commanded them in the Torah through Moshe Rabeinu (Moses). If they keep and perform these Mitzvos (laws) out of intellectual conviction and as logical guidelines for the survival of the world, they are not a resident alien (Ger Toshav), nor of the Pious among the Gentiles (Chasid Umot HaOlam), nor of their wise men.
When a Ben Noach fulfills a Mitzvah of the Torah that is not prohibited to him, he receives the reward of an 'Eino Metzuveh v'Oseh' - 'one who performs a Mitzvah in which he was not commanded.' This reward is less than the reward of one who performs Mitzvos in which he was commanded (Gemara Bava Kama 38a, Kidushin 31a).
According to the Rambam's Hilchos Melachim
Avodah Zarah - Idolatry - עבודה זרה
A gentile who worships false gods is liable to the death penalty, provided he worships them in the regular form in which that particular deity is usually worshiped. A gentile is executed for every type of foreign worship which a Jewish court would consider worthy of capital punishment. However, a gentile is not executed for a type of foreign worship which a Jewish court would not deem worthy of capital punishment. Nevertheless, even though a gentile will not be executed for these forms of worship, he is forbidden to engage in all of them. They are not allow them to erect a monument, or to plant an asherah, or to make images and the like, even though they are only for the sake of beauty.
Birchat HaShem - Blasphemy - ברכת השם
A gentile who curses God's Name, whether he uses God's unique Name or one of His other names, in any language, is liable to the death penalty. Blasphemy with one of the attributes of God's name is an action which, if committed by an Israelite, would not be regarded as criminal (Sanhedrin 56b).
Dinim - Justice - הדינים
The Noachidæ are required to establish courts of justice in every city and province; and these courts are to judge the people with regard to the six laws and to warn them against the transgression of any of them (Rambam, Hilchos Melakim 9:14, 10:11; comp. Nachmanides on Gen. 34:13, where the opinion is expressed that these courts should judge also cases other than those coming under the head of the six laws, as, for example, larceny, assault and battery, etc.). A gentile who transgresses one of these Seven Mitzvot shall be executed by decapitation. A gentile is executed on the basis of the testimony of one witness and the verdict of a single judge. No prior warning is required. Relatives may serve as witnesses. However, a woman may not serve as a witness or a judge for them.
Shefichat Damim - Murder - שפיכות דמים
A gentile who slays a human being, even a fetus in its mother's womb, must be executed in retribution for its death. Similarly, if he slew a person who would have otherwise died in the near future or killed a person whose life is despaired of, or tied up and placed someone before a lion , or starved a person to death, he should be executed , for he has committed murder in one manner or other. Similarly, a pursuer should be executed if he kills the person he is chasing when he could have saved the latter's potential victim by maiming one of the attacker's limbs. Under the same circumstances an Israelite would not be executed. (Sanhedrin 57b; Rambam, Hilchos Melakim 9:4; comp. Kesef Mishneh, ad loc.).